Short RC column (load factor method): According to the load factor method, the permissible axial load W on a short reinforced concrete column with longitudinal bars and lateral stirrups is taken as which of the following?

Introduction / Context:
Axial load capacity of short columns in reinforced concrete arises from both concrete and longitudinal steel. The load factor (working stress–type) approach sums the contributions of each material at their permissible stresses to estimate allowable axial load.

Given Data / Assumptions:

• Short column (buckling effects neglected).
• Longitudinal bars with lateral ties (stirrups) for confinement.
• Use of permissible (allowable) stresses for concrete and steel.

Concept / Approach:
The basic expression is W_allowable = σ_c,perm * A_c + σ_s,perm * A_s, where σ_c,perm and σ_s,perm are the permissible compressive stresses for concrete and steel respectively, A_c is net concrete area (gross minus steel), and A_s is area of longitudinal steel. Reduction factors for slenderness or eccentricity apply as required by design provisions.

Step-by-Step Solution:
Identify material permissible stresses.Compute areas A_c and A_s.Sum contributions: W = σ_c,perm * A_c + σ_s,perm * A_s.

Verification / Alternative check:
Limit state design (ultimate strength method) uses factored loads and strengths with different equations; however, under the load factor / working stress framing of this question, the linear addition of permissible stress contributions is correct for short columns under concentric load.

Why Other Options Are Wrong:
Options a and b consider only one material, underestimating capacity.Option d dismisses the established expression.

Common Pitfalls:

• Forgetting to reduce A_c by A_s when computing concrete contribution.
• Ignoring eccentricity, which reduces permissible load.

Final Answer:
Stress in concrete × Area of concrete + Stress in steel × Area of steel